Drifting patterns as field reversals

Abstract

One-dimensional patterns generated by the Faraday instability at the surface of a vertically vibrated fluid are investigated when the reflection symmetry in the direction of the pattern is broken. For large symmetry breaking, the stationary instability turns into a Hopf bifurcation at a codimension-2 point. This Hopf bifurcation amounts to a periodic drift of the pattern. Further above the onset of the instability, this drift transition competes with the Eckhaus instability as predicted by the study of a model built upon the Swift-Hohenberg equation. In the presence of noise, the drift becomes random and time series of the pattern amplitude display random reversals (sign changes). We show that these reversals belong to the same class as those observed in a variety of contexts such as magnetic fields generated by dynamo action.